Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

Unit 7: Quadratics

Name: ________________________ Lesson 7.1 - The Parabola Graphing quadratic functions by hand 1) The Basic Shape

x y 0 1 2 3 -1 -2 -3

2) The Horizontal Shift

Example: if The equation is

x y

CONCLUSION: The variable will move the parabola _________

y = x2

y = (x − p)2

p = 4

y = (x − 4)2

p

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

3) The Vertical Shift

Example: if The equation is

x y

CONCLUSION: The variable will move the parabola _________ 4) The Stretch Factor

Examples: if

The equations are

x y x y

CONCLUSION: The variable will __________ the parabola

y = x2 + q

q = 4

y = x2 + 4

q

y = ax2

a = 2,  or a = 12

y = 2x2 ,  y = 12x2

a

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

5) Negative Examples: if The equation is now

x y

CONCLUSION: The negative will __________ the parabola

Putting it all together

= ____________________ = ____________________ = ____________________

= ____________________

a

a = −1

y = −x2

a

y = a(x − p)2 + qpqa

(p,q)

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

Example: Analyze the following quadratic before graphing:

a) p = _____ q = _____ b) where will the vertex of the parabola be? ____________ c) has the parabola been compressed vertically or stretched vertically? ____________ d) does the parabola have a maximum or a minimum? ____________ e) make a table of values, starting with the vertex and including three points on each side.

x y

f) graph the parabola

y =12(x − 3)2 − 4

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

Assignment Starting with the vertex, use 2-4 more points in each direction to accurately draw the

following quadratics and fill out the chart below 1) 𝑦 = 𝑥! − 2

2) 𝑦 = (𝑥 − 2)!

3) 𝑦 = −(𝑥 + 1)! + 2

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

4) 𝑦 = !!(𝑥 + 2)! − 2

5) 𝑦 = − !!(𝑥 − 2)! + 3

6) 𝑦 = −2(𝑥 − 1)! − 2

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

7) 𝑦 − 4 = − !!(𝑥 + 2)!

8) 𝑦 + 3 = !!(𝑥 − 4)!

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

x y Horizontal shift (p)

Vertical shift (q)

Vertex

Stretch factor (a)

Compressed Vertically OR Stretched Vertically

Minimum (opens up) OR Maximum (opens down)

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

Answer Key

1) 2)

3) 4)

5) 6)

7) 8)

Foundations of Math 11: Unit 7 – Quadratics Sardis Secondary

Foundationsmath11.weebly.com Mr. Sutcliffe

Practice Quiz Draw the parabola using at least seven points:

21 ( 2) 42

y x= − −

x y